title: Incidence and density relationships of powdery mildew on apple.
abstract: ABSTRACT The relationships between disease incidence and colony density and between leaf and shoot disease incidences for apple powdery mildew were investigated over four seasons in order to derive a simple relationship for predicting density using incidence. The Neyman type A distribution generally provided a good fit to the observed number of colonies per leaf and shoot, and provided a significantly better fit than the Poisson distribution, indicating a degree of aggregation of mildew colonies. In general, Taylor's power-law satisfactorily described the observed variance-mean relationship for colony density; however, Taylor's power-law broke down at very high levels of mean density. Incidence of leaf infection could be determined based on average number of colonies per leaf assuming a fixed variance-mean relationship and a Neyman type A distribution for colony density. Regression models using the complemen- tary log-log transformation of incidence also provided accurate predictions of leaf (or shoot) disease incidence from colonies per leaf (or per shoot). Similar accuracies of these incidence-density models suggested that variance-mean ratio of colony density was more or less constant over time. Unlike the case with colony density, the number of mildewed leaves per shoot generally had a random pattern, as indicated by the good fit of the binomial distribution. Thus, it was possible to estimate the leaf incidence of the youngest unrolled leaves on a shoot using the shoot incidence. It is argued that the leaf incidence-density relationships developed in the present study may be used in making practical disease management decisions.
authors.forename: Xiangming
authors.initials: X
authors.lastname: Xu
authors.forename: Laurence V
authors.initials: LV
authors.lastname: Madden